Results 1  10
of
36
An Efficient Implementation Of A Scaling MinimumCost Flow Algorithm
 Journal of Algorithms
, 1992
"... . The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well o ..."
Abstract

Cited by 121 (6 self)
 Add to MetaCart
(Show Context)
. The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well over a wide range of problem classes. In our experiments, it was always competitive with the established codes, and usually outperformed these codes by a wide margin. Some heuristics we develop may apply to other network algorithms. Our experimental work on the minimumcost flow problem motivated theoretical work on related problems. Supported in part by ONR Young Investigator Award N0001491J1855, NSF Presidential Young Investigator Grant CCR8858097 with matching funds from AT&T and DEC, Stanford University Office of Technology Licensing, and a grant form the Powell Foundation. 1 1. Introduction. Significant theoretical progress has been made recently in the area of minimumcost flow ...
Continuation and Path Following
, 1992
"... CONTENTS 1 Introduction 1 2 The Basics of PredictorCorrector Path Following 3 3 Aspects of Implementations 7 4 Applications 15 5 PiecewiseLinear Methods 34 6 Complexity 41 7 Available Software 44 References 48 1. Introduction Continuation, embedding or homotopy methods have long served as useful ..."
Abstract

Cited by 84 (6 self)
 Add to MetaCart
CONTENTS 1 Introduction 1 2 The Basics of PredictorCorrector Path Following 3 3 Aspects of Implementations 7 4 Applications 15 5 PiecewiseLinear Methods 34 6 Complexity 41 7 Available Software 44 References 48 1. Introduction Continuation, embedding or homotopy methods have long served as useful theoretical tools in modern mathematics. Their use can be traced back at least to such venerated works as those of Poincar'e (18811886), Klein (1882 1883) and Bernstein (1910). Leray and Schauder (1934) refined the tool and presented it as a global result in topology, viz., the homotopy invariance of degree. The use of deformations to solve nonlinear systems of equations Partially supported by the National Science Foundation via grant # DMS9104058 y Preprint, Colorado State University, August 2 E. Allgower and K. Georg may be traced back at least to Lahaye (1934). The classical embedding methods were the
A case study of multiservice, multipriority traffic engineering design for data networks
 Global Telecommunications Conference (GLOBECOM ’99
, 1999
"... ..."
(Show Context)
A QMRbased interiorpoint algorithm for solving linear programs
 Math. Programming
, 1997
"... ..."
(Show Context)
A Truncated PrimalInfeasible DualFeasible Network Interior Point Method
, 1994
"... . In this paper we introduce the truncated primalinfeasible dualfeasible interior point algorithm for linear programming and describe an implementation of this algorithm for solving the minimum cost network flow problem. In each iteration, the linear system that determines the search direction is ..."
Abstract

Cited by 29 (3 self)
 Add to MetaCart
(Show Context)
. In this paper we introduce the truncated primalinfeasible dualfeasible interior point algorithm for linear programming and describe an implementation of this algorithm for solving the minimum cost network flow problem. In each iteration, the linear system that determines the search direction is computed inexactly, and the norm of the resulting residual vector is used in the stopping criteria of the iterative solver employed for the solution of the system. In the implementation, a preconditioned conjugate gradient method is used as the iterative solver. The details of the implementation are described and the code, pdnet, is tested on a large set of standard minimum cost network flow test problems. Computational results indicate that the implementation is competitive with stateoftheart network flow codes. Key Words. Interior point method, linear programming, network flows, primalinfeasible dualfeasible, truncated Newton method, conjugate gradient, maximum flow, experimental test...
Implementation of a Combinatorial Multicommodity Flow Algorithm
, 1992
"... The multicommodity flow problem involves simultaneously shipping multiple commodities through a single network so that the total amount of flow on each edge is no more than the capacity of the edge. This problem can be expressed as a large linear program, and most known algorithms for it, both theor ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
The multicommodity flow problem involves simultaneously shipping multiple commodities through a single network so that the total amount of flow on each edge is no more than the capacity of the edge. This problem can be expressed as a large linear program, and most known algorithms for it, both theoretical and practical, are linear programming algorithms designed to take advantage of the structure of multicommodity flow problems. The size of the linear programs, however, makes it prohibitively difficult to solve large multicommodity flow problems. In this paper, we describe and examine a multicommodity flow implementation based on the recent combinatorial approximation algorithm of Leighton et al. [13]. The theory predicts that the running time of the algorithm increases linearly with the number of commodities. Our experiments verify this behavior. The theory also predicts that the running time increases as the square of the desired precision. Our experiments show that the running time ...
A Class of Preconditioners for Weighted Least Squares Problems
, 1999
"... We consider solving a sequence of weighted linear least squares problems where the changes from one problem to the next are the weights and the right hand side (or data). This is the case for primaldual interiorpoint methods. We derive a class of preconditioners based on a low rank correction to a ..."
Abstract

Cited by 18 (11 self)
 Add to MetaCart
We consider solving a sequence of weighted linear least squares problems where the changes from one problem to the next are the weights and the right hand side (or data). This is the case for primaldual interiorpoint methods. We derive a class of preconditioners based on a low rank correction to a Cholesky factorization of a weighted normal equation coefficient matrix with the previous weight. Key Words. Weighted linear least squares, Preconditioners, Preconditioned conjugate gradient for least squares, Linear programming, Primaldual infeasibleinteriorpoint algorithms. 1 Introduction In this paper, we present a class of preconditioners based on low rank corrections to the Cholesky factorization of a weighted normal equation coefficient matrix. This class of preconditioners leads to good performance for interiorpoint methods for linear programming. Particularly, we have implemented primaldual Newton method to test this class of preconditioners. The numerical results on large scale...
INTERIOR POINT METHODS FOR COMBINATORIAL OPTIMIZATION
, 1995
"... Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivale ..."
Abstract

Cited by 16 (9 self)
 Add to MetaCart
(Show Context)
Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow problems, and methods for solving multicommodity flow problems, including an interior point column generation algorithm.
Adaptive Use of Iterative Methods in PredictorCorrector Interior Point Methods for Linear Programming
 NUMERICAL ALGORITHMS
, 1999
"... ..."
(Show Context)
Adaptive Use Of Iterative Methods In Interior Point Methods For Linear Programming
, 1995
"... In this work we devise efficient algorithms for finding the search directions for interior point methods applied to linear programming problems. There are two innovations. The first is the use of updating of preconditioners computed for previous barrier parameters. The second is an adaptive automate ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
In this work we devise efficient algorithms for finding the search directions for interior point methods applied to linear programming problems. There are two innovations. The first is the use of updating of preconditioners computed for previous barrier parameters. The second is an adaptive automated procedure for determining whether to use a direct or iterative solver, whether to reinitialize or update the preconditioner, and how many updates to apply. These decisions are based on predictions of the cost of using the different solvers to determine the next search direction, given costs in determining earlier directions. These ideas are tested by applying a modified version of the OB1R code of Lustig, Marsten, and Shanno to a variety of problems from the NETLIB and other collections. If a direct method is appropriate for the problem, then our procedure chooses it, but when an iterative procedure is helpful, substantial gains in efficiency can be obtained.